Abstract

VALDES-PARADA, Francisco J.. Integral formulation for the solution of closure problems in upscaling processes. Rev. Mex. Ing. Quím [online]. 2010, vol.9, n.1, pp.53-66. ISSN 1665-2738.

The derivation of transport models at macroscopic scales can be carried out using upscaling techniques such as the method of volume averaging. This upscaling technique consists on averaging the transport equations that describe phenomena at the microscale. The result is the so-called effective medium models, which are expressed in terms of effective coeffcients that can be computed from the solution of the corresponding closure problems. In this work, we present an integral formulation based on Green’s functions to carry out the formal solution of closure problems. This methodology not only provides a physical interpretation of the closure variables, but it also allows solving nonlinear closure problems. In addition, the integral formulation only requires the solution of one boundary-value problem; this represents an advantage with respect to the traditional approach. The results from this work extend the range of applicability of the method of volume averaging to nonlinear problems by associating the linear part of the closure problem to the Green’s function and considering the nonlinear part as a nonhomogeneous source.

Keywords : integral formulation; Green’s function; upscaling; closure problem.

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